Invariant Measures

Share this page

John von Neumann

In 1940–1941 von Neumann lectured on invariant measures at the Institute for
Advanced Study at Princeton. This book is essentially a written version of
those lectures.

The lectures began with general measure theory and went on to Haar measure and
some of its generalizations. Shizuo Kakutani was at the Institute that year,
and he and von Neumann had many conversations on the subject. The conversations
revealed facts and produced proofs. Quite a bit of the content of the course,
especially toward the end, was discovered a few weeks before it appeared on the
blackboard. The original version of these notes was prepared by Paul Halmos,
von Neumann's assistant that year. Von Neumann read the handwritten version
before it went to the typist and sometimes scribbled comments on the margins;
he rewrote most of Chapter 6. This book is the first published version of the
original notes.

Readership

Graduate students and research mathematicians working in classical
measure theory and analysis on general topological groups.

Reviews & Endorsements

The present American Mathematical Society publication essentially
represents a collection of lectures given by von Neumann at the Institute
for Advanced Study during 1940–41. Although the material is foundational,
important, and is the basis for various graduate texts, it serves the
purpose of both history and usefulness to have it available under one cover.

Table of Contents

Invariant Measures

In 1940–1941 von Neumann lectured on invariant measures at the Institute for
Advanced Study at Princeton. This book is essentially a written version of
those lectures.

The lectures began with general measure theory and went on to Haar measure and
some of its generalizations. Shizuo Kakutani was at the Institute that year,
and he and von Neumann had many conversations on the subject. The conversations
revealed facts and produced proofs. Quite a bit of the content of the course,
especially toward the end, was discovered a few weeks before it appeared on the
blackboard. The original version of these notes was prepared by Paul Halmos,
von Neumann's assistant that year. Von Neumann read the handwritten version
before it went to the typist and sometimes scribbled comments on the margins;
he rewrote most of Chapter 6. This book is the first published version of the
original notes.

Graduate students and research mathematicians working in classical
measure theory and analysis on general topological groups.

Reviews:

The present American Mathematical Society publication essentially
represents a collection of lectures given by von Neumann at the Institute
for Advanced Study during 1940–41. Although the material is foundational,
important, and is the basis for various graduate texts, it serves the
purpose of both history and usefulness to have it available under one cover.